[PDF] Top 20 Results on uniqueness of meromorphic functions of differential polynomial

... non-constant meromorphic function, n be a positive integer and a(6≡ 0, ∞) be a meromorphic function satisfying T (r, a) = o(T (r , f )) as r → ...constant differential polynomial in f ... See full document

... some uniqueness theorems of two transcendental meromorphic functions with their nonlinear di ff erential polynomials sharing a small ...These results in this paper improve those given by ... See full document

... Abstract In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function.. Ke[r] ... See full document

... a uniqueness theorem of meromorphic functions whose some nonlinear differential shares 1 IM with powers of the meromor- phic functions, where the degrees of the powers are equal to ... See full document

... The uniqueness theory of meromorphic functions mainly studies conditions under which there is a unique function satisfying the given ...cal results in this field can be seen in [10], where ... See full document

... the uniqueness of meromorphic functions whose differential polynomial share a non-zero finite ...The results in this paper improve some results given by Fang ... See full document

... Lemma 2.10 [15] Let f and g be non-constant meromorphic functions, , n k be two positive integers with n > + k 2 , and let P w ( ) be defined as in (1.1), a z ( ) ( ≡ ∞ / 0, ) be a small function with ... See full document

... Theorem C see 6. Let fz and gz be two nonconstant entire functions, and let n, m, k be three positive integers such that n > 5k 4m 9. If f n zfz − 1 m k and g n zgz − 1 m k share 1 IM, then either fz ≡ gz or f ... See full document

... of meromorphic functions (see ...the uniqueness results of difference polynomials of meromorphic functions, their shifts and difference operators (see ...transcendental ... See full document

... and uniqueness of com- plex difference polynomials of meromorphic ...fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions ... See full document

... of meromorphic functions in the open com- plex plane C; in , by considering the unicity of an entire function f and its first order derivative f , Rubel and Yang [] showed that f ≡ f when they share two ... See full document

... the uniqueness problems on meromorphic functions sharing nonzero finite value or having fixed ...Our results extend the corresponding results of Fang and Hua, Yang and Hua, and Fang and ... See full document

... the uniqueness of an entire function sharing one finite value with its ...entire functions of finite order sharing a periodic small function to f ...of meromorphic functions of finite order ... See full document

... two meromorphic functions defined in C, there are many uniqueness theorems when they share small functions az is called a small function of fz if T r, az oT r, f r → ∞ see ...similar ... See full document

... of meromorphic functions occupies one of the central places in complex ...important uniqueness theorems in the complex plane to the subset X (including the unit disc, the angular domain, the annu- ... See full document

... It is well known that if f and g share four distinct values CM, then f is a fractional transformation of g. In 1997, corresponding to one famous question of Hayman, C. C. Yang and X. H. Hua showed the similar conclusions ... See full document

... of meromorphic functions which involves differential polynomial sharing ...two results: Let k be a positive integer, b (= 0) be a complex number, and h(z) be a polynomial with degree at ... See full document

... A recent increment to uniqueness theory has been to considering weighted shar- ing instead of sharing IM/CM which implies a gradual change from sharing IM to sharing CM. This notion of weighted sharing has been ... See full document

... the uniqueness problems on the case that shifts or differ- ence polynomials of two entire functions share a small ...the uniqueness problems of difference operators of meromorphic ... See full document

... ferential polynomial f n (f − 1)f 0 , Fang [15] showed that f n (f − 1)f 0 assumes every non-zero value a ∈ C infinitely often for n ≥ ...following uniqueness theorem due to Lin and Yi [16, ... See full document